He's famous mainly for being a movie star. Much less, but still famous, for the "martial art" he created, at a time when everyone was still into the traditional styles, working their Katas and whatnot. His objective was efficiency; hence the name Jeet Kune Do (The Way of the Intercepting Fist). I've been taking JKD lessons for almost 3 years now, and I've learned a lot about Bruce and the style (without a style) he created.
So what if he wasn't the best martial artist? What he did to contribute to the world with his ideas is what he should be remembered for. His top students are probably better practitioners than he ever was, but it doesn't mean his legacy should be shoved aside.
But to answer your question, the only fight I'm aware of, other than ones in Hong Kong, is the fight he had against a local instructor for the rights to teach Wing Chun to Americans. According to his students at the time, who are still alive and teaching, this fight is what led him to create a more efficient take on the martial arts he already knew. Also, Jackie Chan is super famous for the movies he's been in, but he probably won't become a legend unless he does something extraordinary, like Bruce.